Suppose D = | array lll a _ 1 & ~b _ 1 & c _ 1 a _ 2 & ~b _ 2 & c _ 2 a _ 3 & ~b _ 3 & c _ 3 array | and D’ = | array lll a _ 1 + p _ 1 & ~b _ 1 + q _ 1 & c _ 1 + a _ 1 a _ 2 + p _ 2 & ~b _ 2 + q _ 2 & c _ 2 + n _ 2 a _ 3 + p _ 3 & ~b _ 3 + q _ 3 & c _ 3 + n _ 3 array | . Then

Suppose D = | array lll a _ 1 & ~b _ 1 & c _ 1 a _ 2 & ~b _ 2 & c _ 2 a _ 3 & ~b _ 3 & c…

Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants

Suppose D = \[\left|\begin{array}{lll} \mathrm{a}_{1} & \mathrm{~b}_{1} & \mathrm{c}_{1} \\ \mathrm{a}_{2} & \mathrm{~b}_{2} & \mathrm{c}_{2} \\ \mathrm{a}_{3} & \mathrm{~b}_{3} & \mathrm{c}_{3} \end{array}\right|\] and
D’ =\[\left|\begin{array}{lll} \mathrm{a}_{1}+\mathrm{p}_{1} & \mathrm{~b}_{1}+\mathrm{q}_{1} & \mathrm{c}_{1}+\mathrm{a}_{1} \\ \mathrm{a}_{2}+\mathrm{p}_{2} & \mathrm{~b}_{2}+\mathrm{q}_{2} & \mathrm{c}_{2}+\mathrm{n}_{2} \\ \mathrm{a}_{3}+\mathrm{p}_{3} & \mathrm{~b}_{3}+\mathrm{q}_{3} & \mathrm{c}_{3}+\mathrm{n}_{3} \end{array}\right|\]. Then

D’ = D
D’ = D (1 – pqr)
D’ = D (1 + p + q + r)
D’ = D (1 + pqr)

Answer

(D) D’ = D (1 + pqr)

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Suppose D = | array lll a _ 1 & ~b _ 1 & c _ 1 a _ 2 & ~b _ 2 & c _ 2 a _ 3 & ~b _ 3 & c…

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